A locally conservative,discontinuous least‐squares finite element method for the Stokes equations

Conventional least‐squares finite element methods (LSFEMs) for incompressible flows conserve mass only approximately. For some problems, mass loss levels are large and result in unphysical solutions. In this paper we formulate a new, locally conservative LSFEM for the Stokes equations wherein a discrete velocity field is computed that is point‐wise divergence free on each element. The central idea is to allow discontinuous velocity approximations and then to define the velocity field on each element using a local stream‐function. The effect of the new LSFEM approach on improved local and global mass conservation is compared with a conventional LSFEM for the Stokes equations employing standard C⁰ Lagrangian elements. Copyright © 2011 John Wiley & Sons, Ltd.     

Extending partial representations of circle graphs

The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle graphs, where the input consists of a graph and a partial representation giving some predrawn chords that represent an induced subgraph of . The question is whether one can extend to a representation of the entire graph , that is, whether one can draw the remaining chords into a partially predrawn representation to obtain a representation of . Our main result is an time algorithm for partial representation extension of circle graphs, where is the number of vertices. To show this, we describe the structure of all representations of a circle graph using split decomposition. This can be of independent interest.     

Reaction of 3-azidoisoxazoles with active methylene compounds

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Short-pulse ECR: A source of multiply charged ions

Extensive investigation is now under way in CERN (European Organization for Nuclear Research) in the framework of the Beta Beam project with the aim of gaining insight into neutrino oscillations. It is suggested that the decay of ⁶He nuclei produce neutrino beams accelerated to an energy on the order of 100 GeV/nucleon. To this end, it is necessary to generate short-pulse (30–100 μs) beams of multiply charged ions of this isotope. Conventional ECR-based ion sources seem to be inappropriate for this purpose, since the plasma density grows slowly (for more than a millisecond) in this case compared with the desired pulse duration. A design concept of a short-pulse ECR-based source of multiply charged ions is proposed. In experiments with pumping at frequencies of 37.5 and 75.0 GHz, pulses as short as ∼50 μs were obtained. Good agreement between theory and experiments is demonstrated.     

Nanostructures of surfaces of silica films obtained by sol—gel method in the presence of organic additives

The dependence of the antireflection properties of film coatings deposited on the silicate glass obtained by sol—gel method in the presence of organic additives on the dimensions of nanostructures of the silica films was studied.     

Diamond-related materials as potential new media in separation science

Recent progress in the development of various diamond-related materials (DRMs) has induced a strong interest in their use as a stationary phase in various separation techniques. DRMs meet many requirements for use as a stationary phase in chromatography, including excellent mechanical and chemical stability, high thermal stability, low chemical reactivity of the surface, and biocompatibility. The general physicochemical properties of diamond and the preparation of different types of DRMs are reviewed, and an overview is provided of current and possible future applications in solid-phase extraction and various separation technologies.